R is a convex polygon. Does R have at least 8 sides? (1)

Question

R is a convex polygon. Does R have at least 8 sides? 

(1) Exactly 3 of the interior angles of R are greater than 80 degrees. 
(2) None of the interior angles of R are less than 60 degrees.

UMB · Answer

to me it is E.
Ther is no specific info in neither statements although taken togather.
it can be pentagon hexagon, octagon,....

kevincan · Answer

Any more takers? One of the above answers is correct

ArvGMAT · Answer

A is not sufficient
Pentagon has all five angles at 108 and has 5 sides

B is also insufficient

I say E.

dreamgmat1 · Answer

I think its E .Information is not sufficient

ridhimagupta · Answer

I would say E.
Not enough information to determine.

kevincan · Answer

What do we know about the interior angles of convex polygons?

Sum=
Each angle is less than ---

dred · Answer

In a convex polygon each of the interior angles of the polygon is less than 180 deg.

For a polygon to be 8 sides.
sum of interior angles = 180 deg (n - 2) = 180 x 6 = 1080

1)Exactly 3 int angles are > 80
=> each of the other 5 interior angles are <= 80 deg.

Best case:
Sum of interior angles of the other 3 sides then should be around
1080 - 80x5 = 680

sum of the 3 sides of a convex polygon should be < 180 deg x 3 = 540 deg
This proves that a convex polygon with n=8 (octagon) is not possible.
n >8, 9, 10..... is possible
2.) insufficient info

I'd go with A

vshaunak@gmail.com · Answer

should be 'E'

Stmt1: polygon can be quadrilateral, pentagon, hexagon..etc. So INSUFF

Stmt2: clearly INSUFF

Taking them together: still not enough info to derive the number of sides.
Hence INSUFF

Kevin, what is OA

R is a convex polygon. Does R have at least 8 sides? (1)

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